Theorems · Theorem · ring theory
Matrix.square_of_invertible
∀ {n : Type u_1} {m : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : Fintype m]
[inst_3 : DecidableEq m] {R : Type u_3} [inst_4 : Semiring R] [InvariantBasisNumber R] (M : Matrix n m R)
(N : Matrix m n R), M * N = 1 → N * M = 1 → Fintype.card n = Fintype.card m- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Fintype.cardstatement · cited by 1,386
- InvariantBasisNumberstatement and proof · cited by 13
- card_eq_of_linearEquivproof · cited by 4
- Matrix.toLinearEquivRight'OfInvproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.HomOrthogonal.equiv_of_isoproof · cited by 0